Question

The probability distribution of random variable X: number of heads , when a fair coin is tossed twice is given by

$x$	$0$	$1$	$2$
p(x)	$p_1$	$p_2$	$p_3$

then

• A. $\sum p_i=0$
• B. $\Pi p_i=1$
• C. $\sum p_i=1$
• D. $\sum p_i=3$

Answer 1

Answer: (C)

$\sum p_i=1$

We know that, the probability distribution of a random variable is a list of probabilities associated with each of its possible values.

Suppose a random variable $X$ may take $k$ different values, with the probability that $X=x_i$ defined to be$P(X=x_i)=p_i$.

The probabilities $p_i$ must satisfy the following:

$0\le p_i\le 1$ for each $i$

$p_1+p_2+...+p_k=1.Thatis\sum p_i=1$

Thus if the probability distribution of random variable $X$: number of heads , when a fair coin is tossed twice is given then $\sum p_i=1$